10. Consider an MA process x(n) of order two described by the difference equation x(n) = v(n) + 0.75 v(n − 1) + 0.75 v(n − 2), where v(n) is a zero-mean white-noise process of unit variance. The requirement is to approximate this process by an AR process u(n) of order M. Do this approximation for the following orders: (a) M = 2. (b) M=5. (c) M = 10. Comment on your results. How big would the order M of the AR process u(n) have to be for it to be equivalent to the MA process x(n) exactly?
10. Consider an MA process x(n) of order two described by the difference equation x(n) = v(n) + 0.75 v(n − 1) + 0.75 v(n − 2), where v(n) is a zero-mean white-noise process of unit variance. The requirement is to approximate this process by an AR process u(n) of order M. Do this approximation for the following orders: (a) M = 2. (b) M=5. (c) M = 10. Comment on your results. How big would the order M of the AR process u(n) have to be for it to be equivalent to the MA process x(n) exactly?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
7
![10. Consider an MA process x(n) of order two described by the difference equation
x(n) = v(n) + 0.75 v(n – 1) + 0.75 v(n – 2),
where v(n) is a zero-mean white-noise process of unit variance. The requirement is to approximate
this process by an AR process u(n) of order M. Do this approximation for the following orders:
(a) M=2.
(b) М -5.
(с) М— 10.
Comment on your results. How big would the order M of the AR process u(n) have to be for
it to be equivalent to the MA process x(n) exactly?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40fcc70f-775e-4741-8507-dd44e1e11495%2F0411c7b2-1646-41d2-9b4e-0b14d38551d3%2Fzdk4xzo_processed.png&w=3840&q=75)
Transcribed Image Text:10. Consider an MA process x(n) of order two described by the difference equation
x(n) = v(n) + 0.75 v(n – 1) + 0.75 v(n – 2),
where v(n) is a zero-mean white-noise process of unit variance. The requirement is to approximate
this process by an AR process u(n) of order M. Do this approximation for the following orders:
(a) M=2.
(b) М -5.
(с) М— 10.
Comment on your results. How big would the order M of the AR process u(n) have to be for
it to be equivalent to the MA process x(n) exactly?
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman